When has your backhand 'broken down'?

If you hit a weak forehand that sits up in the middle of the service box and your opponent blasts an inside out forehand so hard to your backhand that you can barely reach it with the tip of the frame when all-out sprinting and stretching for it, thus you make a backhand error, has your backhand broken down?

If your opponent smashes at your body (vaguely at your backhand), and you fail to get out of the way in time to hit a backhand, thus making a backhand error, has your backhand broken down?

If your opponent hits a really sharply angled volley to your backhand, forcing you to come up with a passing shot winner on the dead run, and you fail to pass (you hit it so that he can volley away for a winner) - has your backhand broken down?

Basically, does any sort of error from the backhand, regardless of situation, mean that your backhand has 'broken down'?

None of the above..a stoke has broken down when you miss a shot because you hit with flawed technique you wouldn't normally use. For example, if you hit a normal rally ball into the bottom of the net, your shot probably broke down somehow.

personally, I know I can recognize when it was the opponents tough shot that caused me problems, and when "my shot broke down" that caused the error.

... in fact, I would say that out of 100 misses, only about 5 of them would I say "Wow? Not sure what happened there... that felt pretty good." All the rest I could attribute to a forced error or unforced error (which IMO would include hitting just deep because I tried to hit to close to the baseline, or hit it into the top of the net because I tried to cut it too close- those IMO aren't really breakdowns in the stroke as much as they are breakdowns in my over-confidence in trying for an outright winner vs a steadier, safer return.)

In my opinion, generally no. A shot breaking down, IMO, generally means that you're missing shots that you should make. An opponent breaking down one of your shots has the added element that they're doing something that makes the shot just a bit more difficult. You should be able to hit it, but because of pace, spin, placement, they make it just enough tougher that you start missing more often.

The classic example is kicking up inside out fh to an opponent's bh. Safe shot for the player hitting fhs, potentially difficult shot for the player hitting bhs because of pace and spin. He's there, he's set-up to hit, but it's a harder shot.

The situations that you've described in your OP fall more into the category that you've thrown up a weak ball and are now paying the price.

It's only broken when it doesn't hit anywhere near a normal backhand.
If opponent crushes a ball at your backhand, and your skill level doesn't allow you to reply with an ATP level winner, your backhand did not break down, YOU did. You haven't the skills to hit this shot, and you don't own it.